I have had two bikes which I found in the dumpster (rubbish bin here in Australia).
With some time and elbow grease, and sometimes a little bit of money you can restore a bike which was destined for the dump into something that is fast and fun to ride around.
This instructible shows you how to restore a dumpster bike - in this case a 10-speed road/touring bike. These bikes are commonly thrown out, can be converted into a single speed or easily renovated into a working bike.
I have concentrated mainly on providing the resources and hints, rather than the in-depth detail for each section of the bike. The reason for this is that no two bikes are the same and if I go into too much detail for one part (eg. the headset).
Step 1: Getting Started
Old bikes that no-one wants are plentiful. They can be left out with the hard rubbish, or people cleaning out thier shed, garage sales or antique / bric-a-brac shops. You may be able to barter for a friend's old bike eg. offer to mow their lawn or babysit.
Decide your reasons for doing this project.
This will save you a lot of time and/or heartache in the long run. Some questions to ask yourself:
Why this bike? Check that the bike you have obtained matches up with how you will ride it. The frame size should fit you comfortably, and the style of bike and your use should be well matched. That being said, I have seen a beach cruiser been ridden in a triathlon before! Lots of people restore these bikes so that they have a cheap commuter that is not likely to get stolen compared to their snazzy carbon tri bike for the weekend. It may be your grandpa's old Cro-Mo racer which you want to restore as a moving heirloom.
What are my constraints? You may be pushed for time / space / money. If you would prefer your leisure time spent riding, then you may be better off buying a new bike. It may be more fun to give the bike to someone once you have finished if you are short on space at home.
What is my budget? Another important question. For a clunky commuter bike, you may just want to clean it up and spray it to protect it from rust. For a vintage pista or road racer, it might be worth spending a little money for a comfortable saddle, clip in pedals and bar grips. The money may be better spent on a new bike!
What is the condition of the bike? This is really important. Check the bike to see that it is in repairable condition. Look for things like cracks in the frame, broken spokes / misaligned wheel rims, dull sound when you hit the frame (structural rust) missing cogs on the derailleur, bent forks, seized crank or headset. All of these things can be fixed, but it may be uneconomical to repair them and the bike just won't be the same as if you waited to pour your energy into a dumpster bike that was a little less 'loved'.
Ok, so you have the bike, you have the money and the vision to complete the project. Let's get started!